At Greenwood High School, 50 students took two unit assessments in Mathematics, each scored out of 50 marks. In Assessment 1, the average score of the first 30 students (arranged by ascending ID numbers) was 30, while the average score of the last 30 students was 42. The combined average score of the first 20 and the last 20 students was 36. In Assessment 2, each student's score was calculated relative to their Assessment 1 score: the first 20 students' scores increased by 30%, the next 10 students' scores remained unchanged, and the last 20 students' scores decreased by 30% What was the average score per student (out of 50) in Assessment 2?

Let the sums of the scores for the groups of first 20, middle 10, and last 20 students be S1, S2, and S3 respectively. From Assessment 1, the total for the first 30 students is S1 + S2 = 900, the total for the last 30 is S2 + S3 = 1260, and the combined total for the first 20 and last 20 is S1 + S3 = 1440. Adding all three equations gives 2(S1 + S2 + S3) = 3600, so the total sum of all 50 students is 1800. In Assessment 2, the new total sum becomes 1.3(S1) + 1(S2) + 0.7(S3), which simplifies to 1800 minus 0.3(S1) plus 0.3(S3); substituting S3 = 540 and S1 = 900 from the earlier equations yields a new total of 1692. Dividing this new total sum of 1692 by the 50 students gives an average score of 33.84.

• Thanks
• Wrong explanation